APPLICATION OF RAY THEORY TO 

 LOW FREQUENCY PROPAGATION 



INTRODUCTION 



It is often said that ray theory is not applicable to low frequency propagation 

 in the ocean. The purpose of this report is to demonstrate that this is not the 

 case. If the word "ray" is allowed a more general meaning than that used in the 

 classical sense, then ray tracing is indeed a useful means of modeling low fre- 

 quency propagation. 



Early ray tracing programs were primarily concerned with integrating the 

 ray tracing equations of the next section accurately and efficiently. It is shown 

 that the effect of sound-speed representations on the computed value of propa- 

 gation loss is not as important as is currently believed. The most recent addi- 

 tion to practical ray tracing programs is the asymptotic treatment of caustics. 



In the case of a horizontally stratified ocean, the integral representation 

 may be expanded into a multipath series, each term of which corresponds to a 

 particular ray type. Upon integrating, one obtains the acoustic pressure along 

 the ray. It is important to note that this multipath expansion is exact. The ac- 

 curacy of the final result depends on the method of solving the depth dependent 

 wave equation and evaluating the ray type integrals. 



For low frequency propagation in nearly horizontally stratified oceans, the 

 method of horizontal rays is recommended. Here, the pressure is expressed as 

 a summation of normal modes weighted by amplitudes satisfying horizontal ray 

 tracing equations. 



RAY TRACING EQUATIONS 



Several years ago, the state of the art was described in Officer's^ book on 

 sound transmission. Then, ray tracing involved approximating the solution of 

 the reduced wave equation for the acoustic pressure P 



with the Wentzel-Kramers-Brillouin- Jeffreys (WKBJ) form 



95 



